Evaluate the following integrals and choose the correct option: integral (1)/(sqrt(1-x2)) dx integral (1)/(1+x2) dx

May 5, 2026Mathematics

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May 5, 2026

Answer

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Step 1: Solve Question 1. The integral $\int \frac{1}{\sqrt{1-x^2}} dx$ is a standard integral. $\int \frac{1}{\sqrt{1-x^2}} dx = \sin^{-1}x + C$ Comparing this with the given options, option C matches.

The final answer is $\boxed{C}$

Step 2: Solve Question 2. The integral $\int \frac{1}{1+x^2} dx$ is a standard integral. $\int \frac{1}{1+x^2} dx = \tan^{-1}x + C$

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Quick Answer

Welcome back — been a while! Let's pick up where you left off.
The integral (1)/(sqrt(1-x^2)) dx is a standard integral.
(1)/(sqrt(1-x^2)) dx = ^-1x + C Comparing this with the given options, option C matches.
The final answer is C Step 2: Solve Question 2.

Asked on May 5, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 5, 2026

Welcome back — been a while! Let's pick up where you left off. Step 1: Solve Question 1. The integral (1)/(sqrt(1-x^2)) dx is a standard integral. (1)/(sqrt(1-x^2)) dx = ^-1x + C Comparing this with the given options, option C matches. The final answer is C Step 2: Solve Question 2. The integral (1)/(1+x^2) dx is a standard integral. (1)/(1+x^2) dx = ^-1x + C